[RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Szabolcs Nagy]

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Based on code from https://github.com/ARM-software/optimized-routines/

This patch adds a highly optimized generic implementation of expf,
exp2f, logf, log2f and powf.  The new functions are not only
significantly faster, but are also smaller, more accurate and fix
several correctness issues.  In order to achieve this, the algorithm
uses double precision arithmetic for accuracy, avoids divisions and
uses small table lookups to minimize the polynomials.  Special cases
are handled inline to avoid the unnecessary overhead of wrapper
functions and set errno to POSIX requirements.

The new functions are added under newlib/libm/common and are
currently enabled for AArch64 and AArch32 with VFP format.  The
new functions are written in C99 and do not support non-IEEE
representations, mixed endian doubles or non-standard errno setting.
Targets can enable the new math code by undefining OBSOLETE_MATH.
Targets with a single precision FPU may still prefer the old
implementation. It was not clear what's the best way to add such
alternative math implementations to newlib so this is an RFC
patch and feedback is welcome.

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diff --git a/newlib/libc/include/machine/ieeefp.h b/newlib/libc/include/machine/ieeefp.h
index 11ef0dd03..2df54b45e 100644
--- a/newlib/libc/include/machine/ieeefp.h
+++ b/newlib/libc/include/machine/ieeefp.h
@@ -50,6 +50,9 @@
 	
 */
 
+/* New math code is opt-in for now.  */
+#define OBSOLETE_MATH 1
+
 #if (defined(__arm__) || defined(__thumb__)) && !defined(__MAVERICK__)
 /* ARM traditionally used big-endian words; and within those words the
    byte ordering was big or little endian depending upon the target.
@@ -61,6 +64,7 @@
 # else
 #  define __IEEE_BIG_ENDIAN
 # endif
+# undef OBSOLETE_MATH
 #else
 # define __IEEE_BIG_ENDIAN
 # ifdef __ARMEL__
@@ -75,6 +79,7 @@
 #else
 #define __IEEE_BIG_ENDIAN
 #endif
+#undef OBSOLETE_MATH
 #endif
 
 #ifdef __epiphany__
diff --git a/newlib/libm/common/Makefile.am b/newlib/libm/common/Makefile.am
index 1268e17db..3e2620c7e 100644
--- a/newlib/libm/common/Makefile.am
+++ b/newlib/libm/common/Makefile.am
@@ -18,11 +18,14 @@ fsrc =	sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
 	sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
 	sf_infinity.c sf_isinf.c sf_isinff.c sf_isnan.c sf_isnanf.c \
 	sf_log1p.c sf_nan.c sf_nextafter.c sf_pow10.c \
-	sf_rint.c sf_logb.c sf_log2.c \
+	sf_rint.c sf_logb.c \
 	sf_fdim.c sf_fma.c sf_fmax.c sf_fmin.c sf_fpclassify.c \
 	sf_lrint.c sf_llrint.c \
 	sf_lround.c sf_llround.c sf_nearbyint.c sf_remquo.c sf_round.c \
-	sf_scalbln.c sf_trunc.c
+	sf_scalbln.c sf_trunc.c \
+	sf_exp.c sf_exp2.c sf_exp2_data.c sf_log.c sf_log_data.c \
+	sf_log2.c sf_log2_data.c sf_pow_log2_data.c sf_pow.c \
+	math_errf.c
 
 lsrc =	atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \
 	floorl.c log1pl.c expm1l.c acosl.c asinl.c atan2l.c coshl.c sinhl.c \
diff --git a/newlib/libm/common/Makefile.in b/newlib/libm/common/Makefile.in
index 9b367653d..c603be361 100644
--- a/newlib/libm/common/Makefile.in
+++ b/newlib/libm/common/Makefile.in
@@ -78,21 +78,21 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
 	lib_a-s_modf.$(OBJEXT) lib_a-s_scalbn.$(OBJEXT) \
 	lib_a-s_cbrt.$(OBJEXT) lib_a-s_exp10.$(OBJEXT) \
 	lib_a-s_expm1.$(OBJEXT) lib_a-s_ilogb.$(OBJEXT) \
-	lib_a-s_infinity.$(OBJEXT) \
-	lib_a-s_isinf.$(OBJEXT) lib_a-s_isinfd.$(OBJEXT) \
-	lib_a-s_isnan.$(OBJEXT) lib_a-s_isnand.$(OBJEXT) \
-	lib_a-s_log1p.$(OBJEXT) lib_a-s_nan.$(OBJEXT) \
-	lib_a-s_nextafter.$(OBJEXT) lib_a-s_pow10.$(OBJEXT) \
-	lib_a-s_rint.$(OBJEXT) lib_a-s_logb.$(OBJEXT) \
-	lib_a-s_log2.$(OBJEXT) lib_a-s_matherr.$(OBJEXT) \
-	lib_a-s_lib_ver.$(OBJEXT) lib_a-s_fdim.$(OBJEXT) \
-	lib_a-s_fma.$(OBJEXT) lib_a-s_fmax.$(OBJEXT) \
-	lib_a-s_fmin.$(OBJEXT) lib_a-s_fpclassify.$(OBJEXT) \
-	lib_a-s_lrint.$(OBJEXT) lib_a-s_llrint.$(OBJEXT) \
-	lib_a-s_lround.$(OBJEXT) lib_a-s_llround.$(OBJEXT) \
-	lib_a-s_nearbyint.$(OBJEXT) lib_a-s_remquo.$(OBJEXT) \
-	lib_a-s_round.$(OBJEXT) lib_a-s_scalbln.$(OBJEXT) \
-	lib_a-s_signbit.$(OBJEXT) lib_a-s_trunc.$(OBJEXT)
+	lib_a-s_infinity.$(OBJEXT) lib_a-s_isinf.$(OBJEXT) \
+	lib_a-s_isinfd.$(OBJEXT) lib_a-s_isnan.$(OBJEXT) \
+	lib_a-s_isnand.$(OBJEXT) lib_a-s_log1p.$(OBJEXT) \
+	lib_a-s_nan.$(OBJEXT) lib_a-s_nextafter.$(OBJEXT) \
+	lib_a-s_pow10.$(OBJEXT) lib_a-s_rint.$(OBJEXT) \
+	lib_a-s_logb.$(OBJEXT) lib_a-s_log2.$(OBJEXT) \
+	lib_a-s_matherr.$(OBJEXT) lib_a-s_lib_ver.$(OBJEXT) \
+	lib_a-s_fdim.$(OBJEXT) lib_a-s_fma.$(OBJEXT) \
+	lib_a-s_fmax.$(OBJEXT) lib_a-s_fmin.$(OBJEXT) \
+	lib_a-s_fpclassify.$(OBJEXT) lib_a-s_lrint.$(OBJEXT) \
+	lib_a-s_llrint.$(OBJEXT) lib_a-s_lround.$(OBJEXT) \
+	lib_a-s_llround.$(OBJEXT) lib_a-s_nearbyint.$(OBJEXT) \
+	lib_a-s_remquo.$(OBJEXT) lib_a-s_round.$(OBJEXT) \
+	lib_a-s_scalbln.$(OBJEXT) lib_a-s_signbit.$(OBJEXT) \
+	lib_a-s_trunc.$(OBJEXT)
 am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
 	lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
 	lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@@ -102,14 +102,19 @@ am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
 	lib_a-sf_isnanf.$(OBJEXT) lib_a-sf_log1p.$(OBJEXT) \
 	lib_a-sf_nan.$(OBJEXT) lib_a-sf_nextafter.$(OBJEXT) \
 	lib_a-sf_pow10.$(OBJEXT) lib_a-sf_rint.$(OBJEXT) \
-	lib_a-sf_logb.$(OBJEXT) lib_a-sf_log2.$(OBJEXT) \
-	lib_a-sf_fdim.$(OBJEXT) lib_a-sf_fma.$(OBJEXT) \
-	lib_a-sf_fmax.$(OBJEXT) lib_a-sf_fmin.$(OBJEXT) \
-	lib_a-sf_fpclassify.$(OBJEXT) lib_a-sf_lrint.$(OBJEXT) \
-	lib_a-sf_llrint.$(OBJEXT) lib_a-sf_lround.$(OBJEXT) \
-	lib_a-sf_llround.$(OBJEXT) lib_a-sf_nearbyint.$(OBJEXT) \
-	lib_a-sf_remquo.$(OBJEXT) lib_a-sf_round.$(OBJEXT) \
-	lib_a-sf_scalbln.$(OBJEXT) lib_a-sf_trunc.$(OBJEXT)
+	lib_a-sf_logb.$(OBJEXT) lib_a-sf_fdim.$(OBJEXT) \
+	lib_a-sf_fma.$(OBJEXT) lib_a-sf_fmax.$(OBJEXT) \
+	lib_a-sf_fmin.$(OBJEXT) lib_a-sf_fpclassify.$(OBJEXT) \
+	lib_a-sf_lrint.$(OBJEXT) lib_a-sf_llrint.$(OBJEXT) \
+	lib_a-sf_lround.$(OBJEXT) lib_a-sf_llround.$(OBJEXT) \
+	lib_a-sf_nearbyint.$(OBJEXT) lib_a-sf_remquo.$(OBJEXT) \
+	lib_a-sf_round.$(OBJEXT) lib_a-sf_scalbln.$(OBJEXT) \
+	lib_a-sf_trunc.$(OBJEXT) lib_a-sf_exp.$(OBJEXT) \
+	lib_a-sf_exp2.$(OBJEXT) lib_a-sf_exp2_data.$(OBJEXT) \
+	lib_a-sf_log.$(OBJEXT) lib_a-sf_log_data.$(OBJEXT) \
+	lib_a-sf_log2.$(OBJEXT) lib_a-sf_log2_data.$(OBJEXT) \
+	lib_a-sf_pow_log2_data.$(OBJEXT) lib_a-sf_pow.$(OBJEXT) \
+	lib_a-math_errf.$(OBJEXT)
 am__objects_3 = lib_a-atanl.$(OBJEXT) lib_a-cosl.$(OBJEXT) \
 	lib_a-sinl.$(OBJEXT) lib_a-tanl.$(OBJEXT) \
 	lib_a-tanhl.$(OBJEXT) lib_a-frexpl.$(OBJEXT) \
@@ -148,21 +153,23 @@ lib_a_OBJECTS = $(am_lib_a_OBJECTS)
 LTLIBRARIES = $(noinst_LTLIBRARIES)
 libcommon_la_LIBADD =
 am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
-	s_cbrt.lo s_exp10.lo s_expm1.lo s_ilogb.lo \
-	s_infinity.lo s_isinf.lo s_isinfd.lo s_isnan.lo s_isnand.lo \
-	s_log1p.lo s_nan.lo s_nextafter.lo s_pow10.lo s_rint.lo \
-	s_logb.lo s_log2.lo s_matherr.lo s_lib_ver.lo s_fdim.lo \
-	s_fma.lo s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo \
-	s_llrint.lo s_lround.lo s_llround.lo s_nearbyint.lo \
-	s_remquo.lo s_round.lo s_scalbln.lo s_signbit.lo s_trunc.lo
+	s_cbrt.lo s_exp10.lo s_expm1.lo s_ilogb.lo s_infinity.lo \
+	s_isinf.lo s_isinfd.lo s_isnan.lo s_isnand.lo s_log1p.lo \
+	s_nan.lo s_nextafter.lo s_pow10.lo s_rint.lo s_logb.lo \
+	s_log2.lo s_matherr.lo s_lib_ver.lo s_fdim.lo s_fma.lo \
+	s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
+	s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
+	s_scalbln.lo s_signbit.lo s_trunc.lo
 am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
 	sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
 	sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
 	sf_nan.lo sf_nextafter.lo sf_pow10.lo sf_rint.lo sf_logb.lo \
-	sf_log2.lo sf_fdim.lo sf_fma.lo sf_fmax.lo sf_fmin.lo \
-	sf_fpclassify.lo sf_lrint.lo sf_llrint.lo sf_lround.lo \
-	sf_llround.lo sf_nearbyint.lo sf_remquo.lo sf_round.lo \
-	sf_scalbln.lo sf_trunc.lo
+	sf_fdim.lo sf_fma.lo sf_fmax.lo sf_fmin.lo sf_fpclassify.lo \
+	sf_lrint.lo sf_llrint.lo sf_lround.lo sf_llround.lo \
+	sf_nearbyint.lo sf_remquo.lo sf_round.lo sf_scalbln.lo \
+	sf_trunc.lo sf_exp.lo sf_exp2.lo sf_exp2_data.lo sf_log.lo \
+	sf_log_data.lo sf_log2.lo sf_log2_data.lo sf_pow_log2_data.lo \
+	sf_pow.lo math_errf.lo
 am__objects_7 = atanl.lo cosl.lo sinl.lo tanl.lo tanhl.lo frexpl.lo \
 	modfl.lo ceill.lo fabsl.lo floorl.lo log1pl.lo expm1l.lo \
 	acosl.lo asinl.lo atan2l.lo coshl.lo sinhl.lo expl.lo \
@@ -347,11 +354,14 @@ fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
 	sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
 	sf_infinity.c sf_isinf.c sf_isinff.c sf_isnan.c sf_isnanf.c \
 	sf_log1p.c sf_nan.c sf_nextafter.c sf_pow10.c \
-	sf_rint.c sf_logb.c sf_log2.c \
+	sf_rint.c sf_logb.c \
 	sf_fdim.c sf_fma.c sf_fmax.c sf_fmin.c sf_fpclassify.c \
 	sf_lrint.c sf_llrint.c \
 	sf_lround.c sf_llround.c sf_nearbyint.c sf_remquo.c sf_round.c \
-	sf_scalbln.c sf_trunc.c
+	sf_scalbln.c sf_trunc.c \
+	sf_exp.c sf_exp2.c sf_exp2_data.c sf_log.c sf_log_data.c \
+	sf_log2.c sf_log2_data.c sf_pow_log2_data.c sf_pow.c \
+	math_errf.c
 
 lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \
 	floorl.c log1pl.c expm1l.c acosl.c asinl.c atan2l.c coshl.c sinhl.c \
@@ -796,12 +806,6 @@ lib_a-sf_logb.o: sf_logb.c
 lib_a-sf_logb.obj: sf_logb.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_logb.obj `if test -f 'sf_logb.c'; then $(CYGPATH_W) 'sf_logb.c'; else $(CYGPATH_W) '$(srcdir)/sf_logb.c'; fi`
 
-lib_a-sf_log2.o: sf_log2.c
-	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.o `test -f 'sf_log2.c' || echo '$(srcdir)/'`sf_log2.c
-
-lib_a-sf_log2.obj: sf_log2.c
-	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.obj `if test -f 'sf_log2.c'; then $(CYGPATH_W) 'sf_log2.c'; else $(CYGPATH_W) '$(srcdir)/sf_log2.c'; fi`
-
 lib_a-sf_fdim.o: sf_fdim.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_fdim.o `test -f 'sf_fdim.c' || echo '$(srcdir)/'`sf_fdim.c
 
@@ -886,6 +890,66 @@ lib_a-sf_trunc.o: sf_trunc.c
 lib_a-sf_trunc.obj: sf_trunc.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_trunc.obj `if test -f 'sf_trunc.c'; then $(CYGPATH_W) 'sf_trunc.c'; else $(CYGPATH_W) '$(srcdir)/sf_trunc.c'; fi`
 
+lib_a-sf_exp.o: sf_exp.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp.o `test -f 'sf_exp.c' || echo '$(srcdir)/'`sf_exp.c
+
+lib_a-sf_exp.obj: sf_exp.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp.obj `if test -f 'sf_exp.c'; then $(CYGPATH_W) 'sf_exp.c'; else $(CYGPATH_W) '$(srcdir)/sf_exp.c'; fi`
+
+lib_a-sf_exp2.o: sf_exp2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2.o `test -f 'sf_exp2.c' || echo '$(srcdir)/'`sf_exp2.c
+
+lib_a-sf_exp2.obj: sf_exp2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2.obj `if test -f 'sf_exp2.c'; then $(CYGPATH_W) 'sf_exp2.c'; else $(CYGPATH_W) '$(srcdir)/sf_exp2.c'; fi`
+
+lib_a-sf_exp2_data.o: sf_exp2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2_data.o `test -f 'sf_exp2_data.c' || echo '$(srcdir)/'`sf_exp2_data.c
+
+lib_a-sf_exp2_data.obj: sf_exp2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2_data.obj `if test -f 'sf_exp2_data.c'; then $(CYGPATH_W) 'sf_exp2_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_exp2_data.c'; fi`
+
+lib_a-sf_log.o: sf_log.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log.o `test -f 'sf_log.c' || echo '$(srcdir)/'`sf_log.c
+
+lib_a-sf_log.obj: sf_log.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log.obj `if test -f 'sf_log.c'; then $(CYGPATH_W) 'sf_log.c'; else $(CYGPATH_W) '$(srcdir)/sf_log.c'; fi`
+
+lib_a-sf_log_data.o: sf_log_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log_data.o `test -f 'sf_log_data.c' || echo '$(srcdir)/'`sf_log_data.c
+
+lib_a-sf_log_data.obj: sf_log_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log_data.obj `if test -f 'sf_log_data.c'; then $(CYGPATH_W) 'sf_log_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_log_data.c'; fi`
+
+lib_a-sf_log2.o: sf_log2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.o `test -f 'sf_log2.c' || echo '$(srcdir)/'`sf_log2.c
+
+lib_a-sf_log2.obj: sf_log2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.obj `if test -f 'sf_log2.c'; then $(CYGPATH_W) 'sf_log2.c'; else $(CYGPATH_W) '$(srcdir)/sf_log2.c'; fi`
+
+lib_a-sf_log2_data.o: sf_log2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2_data.o `test -f 'sf_log2_data.c' || echo '$(srcdir)/'`sf_log2_data.c
+
+lib_a-sf_log2_data.obj: sf_log2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2_data.obj `if test -f 'sf_log2_data.c'; then $(CYGPATH_W) 'sf_log2_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_log2_data.c'; fi`
+
+lib_a-sf_pow_log2_data.o: sf_pow_log2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow_log2_data.o `test -f 'sf_pow_log2_data.c' || echo '$(srcdir)/'`sf_pow_log2_data.c
+
+lib_a-sf_pow_log2_data.obj: sf_pow_log2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow_log2_data.obj `if test -f 'sf_pow_log2_data.c'; then $(CYGPATH_W) 'sf_pow_log2_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_pow_log2_data.c'; fi`
+
+lib_a-sf_pow.o: sf_pow.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow.o `test -f 'sf_pow.c' || echo '$(srcdir)/'`sf_pow.c
+
+lib_a-sf_pow.obj: sf_pow.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow.obj `if test -f 'sf_pow.c'; then $(CYGPATH_W) 'sf_pow.c'; else $(CYGPATH_W) '$(srcdir)/sf_pow.c'; fi`
+
+lib_a-math_errf.o: math_errf.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_errf.o `test -f 'math_errf.c' || echo '$(srcdir)/'`math_errf.c
+
+lib_a-math_errf.obj: math_errf.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_errf.obj `if test -f 'math_errf.c'; then $(CYGPATH_W) 'math_errf.c'; else $(CYGPATH_W) '$(srcdir)/math_errf.c'; fi`
+
 lib_a-atanl.o: atanl.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-atanl.o `test -f 'atanl.c' || echo '$(srcdir)/'`atanl.c
 
diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h
new file mode 100644
index 000000000..dea981ca9
--- /dev/null
+++ b/newlib/libm/common/math_config.h
@@ -0,0 +1,175 @@
+/* Configuration for math routines.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#ifndef _MATH_CONFIG_H
+#define _MATH_CONFIG_H
+
+#include <math.h>
+#include <stdint.h>
+
+#ifndef WANT_ROUNDING
+/* Correct special case results in non-nearest rounding modes.  */
+#define WANT_ROUNDING 0
+#endif
+#ifndef WANT_ERRNO
+/* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0.  */
+#define WANT_ERRNO 1
+#endif
+#ifndef WANT_ERRNO_UFLOW
+/* Set errno to ERANGE if result underflows to 0 (in all rounding modes).  */
+#define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
+#endif
+
+#ifndef TOINT_INTRINSICS
+#define TOINT_INTRINSICS 0
+#endif
+#ifndef TOINT_RINT
+#define TOINT_RINT 0
+#endif
+#ifndef TOINT_SHIFT
+#define TOINT_SHIFT 1
+#endif
+
+static inline uint32_t
+asuint (float f)
+{
+  union
+  {
+    float f;
+    uint32_t i;
+  } u = {f};
+  return u.i;
+}
+
+static inline float
+asfloat (uint32_t i)
+{
+  union
+  {
+    uint32_t i;
+    float f;
+  } u = {i};
+  return u.f;
+}
+
+static inline uint64_t
+asuint64 (double f)
+{
+  union
+  {
+    double f;
+    uint64_t i;
+  } u = {f};
+  return u.i;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+  union
+  {
+    uint64_t i;
+    double f;
+  } u = {i};
+  return u.f;
+}
+
+static inline int
+ieee_2008_issignaling (float x)
+{
+  uint32_t ix = asuint (x);
+  ix ^= 0x00400000; /* IEEE 754-2008 snan bit.  */
+  return 2 * ix > 2u * 0x7fc00000;
+}
+
+#ifdef __GNUC__
+#define HIDDEN __attribute__ ((__visibility__ ("hidden")))
+#define NOINLINE __attribute__ ((noinline))
+#else
+#define HIDDEN
+#define NOINLINE
+#endif
+
+HIDDEN float __math_oflowf (unsigned long);
+HIDDEN float __math_uflowf (unsigned long);
+HIDDEN float __math_may_uflowf (unsigned long);
+HIDDEN float __math_divzerof (unsigned long);
+HIDDEN float __math_invalidf (float);
+
+/* Shared between expf, exp2f and powf.  */
+#define EXP2F_TABLE_BITS 5
+#define EXP2F_POLY_ORDER 3
+extern const struct exp2f_data
+{
+  uint64_t tab[1 << EXP2F_TABLE_BITS];
+  double shift_scaled;
+  double poly[EXP2F_POLY_ORDER];
+  double shift;
+  double invln2_scaled;
+  double poly_scaled[EXP2F_POLY_ORDER];
+} __exp2f_data;
+
+#define LOGF_TABLE_BITS 4
+#define LOGF_POLY_ORDER 4
+extern const struct logf_data
+{
+  struct
+  {
+    double invc, logc;
+  } tab[1 << LOGF_TABLE_BITS];
+  double ln2;
+  double poly[LOGF_POLY_ORDER];
+} __logf_data;
+
+#define LOG2F_TABLE_BITS 4
+#define LOG2F_POLY_ORDER 4
+extern const struct log2f_data
+{
+  struct
+  {
+    double invc, logc;
+  } tab[1 << LOG2F_TABLE_BITS];
+  double poly[LOG2F_POLY_ORDER];
+} __log2f_data;
+
+#define POWF_LOG2_TABLE_BITS 4
+#define POWF_LOG2_POLY_ORDER 5
+#if TOINT_INTRINSICS
+#define POWF_SCALE_BITS EXP2F_TABLE_BITS
+#else
+#define POWF_SCALE_BITS 0
+#endif
+#define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
+extern const struct powf_log2_data
+{
+  struct
+  {
+    double invc, logc;
+  } tab[1 << POWF_LOG2_TABLE_BITS];
+  double poly[POWF_LOG2_POLY_ORDER];
+} __powf_log2_data;
+
+#endif
diff --git a/newlib/libm/common/math_errf.c b/newlib/libm/common/math_errf.c
new file mode 100644
index 000000000..ccfcc00f2
--- /dev/null
+++ b/newlib/libm/common/math_errf.c
@@ -0,0 +1,89 @@
+/* Single-precision math error handling.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include "math_config.h"
+
+#if WANT_ERRNO
+#include <errno.h>
+/* NOINLINE reduces code size and avoids making math functions non-leaf
+   when the error handling is inlined.  */
+NOINLINE static float
+with_errnof (float y, int e)
+{
+  errno = e;
+  return y;
+}
+#else
+#define with_errnof(x, e) (x)
+#endif
+
+/* NOINLINE prevents fenv semantics breaking optimizations.  */
+NOINLINE static float
+xflowf (unsigned long sign, float y)
+{
+  y = (sign ? -y : y) * y;
+  return with_errnof (y, ERANGE);
+}
+
+HIDDEN float
+__math_uflowf (unsigned long sign)
+{
+  return xflowf (sign, 0x1p-95f);
+}
+
+#if WANT_ERRNO_UFLOW
+/* Underflows to zero in some non-nearest rounding mode, setting errno
+   is valid even if the result is non-zero, but in the subnormal range.  */
+HIDDEN float
+__math_may_uflowf (unsigned long sign)
+{
+  return xflowf (sign, 0x1.4p-75f);
+}
+#endif
+
+HIDDEN float
+__math_oflowf (unsigned long sign)
+{
+  return xflowf (sign, 0x1p97f);
+}
+
+HIDDEN float
+__math_divzerof (unsigned long sign)
+{
+  float y = 0;
+  return with_errnof ((sign ? -1 : 1) / y, ERANGE);
+}
+
+HIDDEN float
+__math_invalidf (float x)
+{
+  float y = (x - x) / (x - x);
+  return isnan (x) ? y : with_errnof (y, EDOM);
+}
+#endif
diff --git a/newlib/libm/common/sf_exp.c b/newlib/libm/common/sf_exp.c
new file mode 100644
index 000000000..477af8e4f
--- /dev/null
+++ b/newlib/libm/common/sf_exp.c
@@ -0,0 +1,113 @@
+/* Single-precision e^x function.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
+Wrong count: 170635 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define InvLn2N __exp2f_data.invln2_scaled
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+  return asuint (x) >> 20;
+}
+
+float
+expf (float x)
+{
+  uint32_t abstop;
+  uint64_t ki, t;
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t kd, xd, z, r, r2, y, s;
+
+  xd = (double_t) x;
+  abstop = top12 (x) & 0x7ff;
+  if (__builtin_expect (abstop >= top12 (88.0f), 0))
+    {
+      /* |x| >= 88 or x is nan.  */
+      if (asuint (x) == asuint (-INFINITY))
+	return 0.0f;
+      if (abstop >= top12 (INFINITY))
+	return x + x;
+      if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
+	return __math_oflowf (0);
+      if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
+	return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+      if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
+	return __math_may_uflowf (0);
+#endif
+    }
+
+  /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
+  z = InvLn2N * xd;
+
+  /* Round and convert z to int, the result is in [-150*N, 128*N] and
+     ideally ties-to-even rule is used, otherwise the magnitude of r
+     can be bigger which gives larger approximation error.  */
+#if TOINT_INTRINSICS
+  kd = roundtoint (z);
+  ki = converttoint (z);
+#elif TOINT_RINT
+  kd = rint (z);
+  ki = (long) kd;
+#elif TOINT_SHIFT
+# define SHIFT __exp2f_data.shift
+  kd = (double) (z + SHIFT); /* Rounding to double precision is required.  */
+  ki = asuint64 (kd);
+  kd -= SHIFT;
+#endif
+  r = z - kd;
+
+  /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+  t = T[ki % N];
+  t += ki << (52 - EXP2F_TABLE_BITS);
+  s = asdouble (t);
+  z = C[0] * r + C[1];
+  r2 = r * r;
+  y = C[2] * r + 1;
+  y = z * r2 + y;
+  y = y * s;
+  return (float) y;
+}
+#endif
diff --git a/newlib/libm/common/sf_exp2.c b/newlib/libm/common/sf_exp2.c
new file mode 100644
index 000000000..5ac5c9b25
--- /dev/null
+++ b/newlib/libm/common/sf_exp2.c
@@ -0,0 +1,99 @@
+/* Single-precision 2^x function.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
+Wrong count: 168353 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly
+#define SHIFT __exp2f_data.shift_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+  return asuint (x) >> 20;
+}
+
+float
+exp2f (float x)
+{
+  uint32_t abstop;
+  uint64_t ki, t;
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t kd, xd, z, r, r2, y, s;
+
+  xd = (double_t) x;
+  abstop = top12 (x) & 0x7ff;
+  if (__builtin_expect (abstop >= top12 (128.0f), 0))
+    {
+      /* |x| >= 128 or x is nan.  */
+      if (asuint (x) == asuint (-INFINITY))
+	return 0.0f;
+      if (abstop >= top12 (INFINITY))
+	return x + x;
+      if (x > 0.0f)
+	return __math_oflowf (0);
+      if (x <= -150.0f)
+	return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+      if (x < -149.0f)
+	return __math_may_uflowf (0);
+#endif
+    }
+
+  /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
+  kd = (double) (xd + SHIFT); /* Rounding to double precision is required.  */
+  ki = asuint64 (kd);
+  kd -= SHIFT; /* k/N for int k.  */
+  r = xd - kd;
+
+  /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+  t = T[ki % N];
+  t += ki << (52 - EXP2F_TABLE_BITS);
+  s = asdouble (t);
+  z = C[0] * r + C[1];
+  r2 = r * r;
+  y = C[2] * r + 1;
+  y = z * r2 + y;
+  y = y * s;
+  return (float) y;
+}
+#endif
diff --git a/newlib/libm/common/sf_exp2_data.c b/newlib/libm/common/sf_exp2_data.c
new file mode 100644
index 000000000..0970e24fb
--- /dev/null
+++ b/newlib/libm/common/sf_exp2_data.c
@@ -0,0 +1,56 @@
+/* Shared data between expf, exp2f and powf.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include "math_config.h"
+
+#define N (1 << EXP2F_TABLE_BITS)
+
+const struct exp2f_data __exp2f_data = {
+  /* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
+     used for computing 2^(k/N) for an int |k| < 150 N as
+     double(tab[k%N] + (k << 52-BITS)) */
+  .tab = {
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+  },
+  .shift_scaled = 0x1.8p+52 / N,
+  .poly = { 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1 },
+  .shift = 0x1.8p+52,
+  .invln2_scaled = 0x1.71547652b82fep+0 * N,
+  .poly_scaled = {
+0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N
+  },
+};
+#endif
diff --git a/newlib/libm/common/sf_log.c b/newlib/libm/common/sf_log.c
new file mode 100644
index 000000000..8b0b8a7e7
--- /dev/null
+++ b/newlib/libm/common/sf_log.c
@@ -0,0 +1,98 @@
+/* Single-precision log function.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+LOGF_TABLE_BITS = 4
+LOGF_POLY_ORDER = 4
+
+ULP error: 0.818 (nearest rounding.)
+Relative error: 1.957 * 2^-26 (before rounding.)
+*/
+
+#define T __logf_data.tab
+#define A __logf_data.poly
+#define Ln2 __logf_data.ln2
+#define N (1 << LOGF_TABLE_BITS)
+#define OFF 0x3f330000
+
+float
+logf (float x)
+{
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t z, r, r2, y, y0, invc, logc;
+  uint32_t ix, iz, tmp;
+  int k, i;
+
+  ix = asuint (x);
+#if WANT_ROUNDING
+  /* Fix sign of zero with downward rounding when x==1.  */
+  if (__builtin_expect (ix == 0x3f800000, 0))
+    return 0;
+#endif
+  if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0))
+    {
+      /* x < 0x1p-126 or inf or nan.  */
+      if (ix * 2 == 0)
+	return __math_divzerof (1);
+      if (ix == 0x7f800000) /* log(inf) == inf.  */
+	return x;
+      if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
+	return __math_invalidf (x);
+      /* x is subnormal, normalize it.  */
+      ix = asuint (x * 0x1p23f);
+      ix -= 23 << 23;
+    }
+
+  /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
+     The range is split into N subintervals.
+     The ith subinterval contains z and c is near its center.  */
+  tmp = ix - OFF;
+  i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
+  k = (int32_t) tmp >> 23; /* arithmetic shift */
+  iz = ix - (tmp & 0x1ff << 23);
+  invc = T[i].invc;
+  logc = T[i].logc;
+  z = (double_t) asfloat (iz);
+
+  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
+  r = z * invc - 1;
+  y0 = logc + (double_t) k * Ln2;
+
+  /* Pipelined polynomial evaluation to approximate log1p(r).  */
+  r2 = r * r;
+  y = A[1] * r + A[2];
+  y = A[0] * r2 + y;
+  y = y * r2 + (y0 + r);
+  return (float) y;
+}
+#endif
diff --git a/newlib/libm/common/sf_log2.c b/newlib/libm/common/sf_log2.c
index 9fbaaca72..caa8f51b1 100644
--- a/newlib/libm/common/sf_log2.c
+++ b/newlib/libm/common/sf_log2.c
@@ -1,48 +1,99 @@
-/* sf_log2.c -- float version of s_log2.c.
- * Modification of sf_exp10.c by Yaakov Selkowitz 2009.
- */
+/* Single-precision log2 function.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
 
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice 
- * is preserved.
- * ====================================================
- */
-
-/* 
- * wrapper log2f(x)
- */
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
 
 #include "fdlibm.h"
-#include <errno.h>
+#ifndef OBSOLETE_MATH
+
 #include <math.h>
-#undef log2
-#undef log2f
-
-#ifdef __STDC__
-	float log2f(float x)		/* wrapper log2f */
-#else
-	float log2f(x)			/* wrapper log2f */
-	float x;
-#endif
-{
-  return (logf(x) / (float_t) M_LN2);
-}
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+LOG2F_TABLE_BITS = 4
+LOG2F_POLY_ORDER = 4
 
-#ifdef _DOUBLE_IS_32BITS
+ULP error: 0.752 (nearest rounding.)
+Relative error: 1.9 * 2^-26 (before rounding.)
+*/
 
-#ifdef __STDC__
-	double log2(double x)
-#else
-	double log2(x)
-	double x;
-#endif
+#define N (1 << LOG2F_TABLE_BITS)
+#define T __log2f_data.tab
+#define A __log2f_data.poly
+#define OFF 0x3f330000
+
+float
+log2f (float x)
 {
-	return (double) log2f((float) x);
-}
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t z, r, r2, p, y, y0, invc, logc;
+  uint32_t ix, iz, top, tmp;
+  int k, i;
+
+  ix = asuint (x);
+#if WANT_ROUNDING
+  /* Fix sign of zero with downward rounding when x==1.  */
+  if (__builtin_expect (ix == 0x3f800000, 0))
+    return 0;
+#endif
+  if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0))
+    {
+      /* x < 0x1p-126 or inf or nan.  */
+      if (ix * 2 == 0)
+	return __math_divzerof (1);
+      if (ix == 0x7f800000) /* log2(inf) == inf.  */
+	return x;
+      if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
+	return __math_invalidf (x);
+      /* x is subnormal, normalize it.  */
+      ix = asuint (x * 0x1p23f);
+      ix -= 23 << 23;
+    }
 
-#endif /* defined(_DOUBLE_IS_32BITS) */
+  /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
+     The range is split into N subintervals.
+     The ith subinterval contains z and c is near its center.  */
+  tmp = ix - OFF;
+  i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
+  top = tmp & 0xff800000;
+  iz = ix - top;
+  k = (int32_t) tmp >> 23; /* arithmetic shift */
+  invc = T[i].invc;
+  logc = T[i].logc;
+  z = (double_t) asfloat (iz);
+
+  /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+  r = z * invc - 1;
+  y0 = logc + (double_t) k;
+
+  /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
+  r2 = r * r;
+  y = A[1] * r + A[2];
+  y = A[0] * r2 + y;
+  p = A[3] * r + y0;
+  y = y * r2 + p;
+  return (float) y;
+}
+#endif
diff --git a/newlib/libm/common/sf_log2_data.c b/newlib/libm/common/sf_log2_data.c
new file mode 100644
index 000000000..844c93633
--- /dev/null
+++ b/newlib/libm/common/sf_log2_data.c
@@ -0,0 +1,56 @@
+/* Data definition for log2f.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include "math_config.h"
+
+const struct log2f_data __log2f_data = {
+  .tab = {
+  { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 },
+  { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 },
+  { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 },
+  { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 },
+  { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 },
+  { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 },
+  { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 },
+  { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 },
+  { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 },
+  { 0x1p+0, 0x0p+0 },
+  { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 },
+  { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 },
+  { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 },
+  { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 },
+  { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 },
+  { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 },
+  },
+  .poly = {
+  -0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1,
+  0x1.715475f35c8b8p0,
+  }
+};
+#endif
diff --git a/newlib/libm/common/sf_log_data.c b/newlib/libm/common/sf_log_data.c
new file mode 100644
index 000000000..e00226aff
--- /dev/null
+++ b/newlib/libm/common/sf_log_data.c
@@ -0,0 +1,56 @@
+/* Data definition for logf.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include "math_config.h"
+
+const struct logf_data __logf_data = {
+  .tab = {
+  { 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 },
+  { 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 },
+  { 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 },
+  { 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 },
+  { 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 },
+  { 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 },
+  { 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 },
+  { 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 },
+  { 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 },
+  { 0x1p+0, 0x0p+0 },
+  { 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 },
+  { 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 },
+  { 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 },
+  { 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 },
+  { 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 },
+  { 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 },
+  },
+  .ln2 = 0x1.62e42fefa39efp-1,
+  .poly = {
+  -0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2,
+  }
+};
+#endif
diff --git a/newlib/libm/common/sf_pow.c b/newlib/libm/common/sf_pow.c
new file mode 100644
index 000000000..51d2069be
--- /dev/null
+++ b/newlib/libm/common/sf_pow.c
@@ -0,0 +1,230 @@
+/* Single-precision pow function.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+POWF_LOG2_POLY_ORDER = 5
+EXP2F_TABLE_BITS = 5
+
+ULP error: 0.82 (~ 0.5 + relerr*2^24)
+relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
+relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
+relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
+*/
+
+#define N (1 << POWF_LOG2_TABLE_BITS)
+#define T __powf_log2_data.tab
+#define A __powf_log2_data.poly
+#define OFF 0x3f330000
+
+/* Subnormal input is normalized so ix has negative biased exponent.
+   Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set.  */
+static inline double_t
+log2_inline (uint32_t ix)
+{
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t z, r, r2, r4, p, q, y, y0, invc, logc;
+  uint32_t iz, top, tmp;
+  int k, i;
+
+  /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
+     The range is split into N subintervals.
+     The ith subinterval contains z and c is near its center.  */
+  tmp = ix - OFF;
+  i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
+  top = tmp & 0xff800000;
+  iz = ix - top;
+  k = (int32_t) top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
+  invc = T[i].invc;
+  logc = T[i].logc;
+  z = (double_t) asfloat (iz);
+
+  /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+  r = z * invc - 1;
+  y0 = logc + (double_t) k;
+
+  /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
+  r2 = r * r;
+  y = A[0] * r + A[1];
+  p = A[2] * r + A[3];
+  r4 = r2 * r2;
+  q = A[4] * r + y0;
+  q = p * r2 + q;
+  y = y * r4 + q;
+  return y;
+}
+
+#undef N
+#undef T
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
+
+/* The output of log2 and thus the input of exp2 is either scaled by N
+   (in case of fast toint intrinsics) or not.  The unscaled xd must be
+   in [-1021,1023], sign_bias sets the sign of the result.  */
+static inline double_t
+exp2_inline (double_t xd, unsigned long sign_bias)
+{
+  uint64_t ki, ski, t;
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t kd, z, r, r2, y, s;
+
+#if TOINT_INTRINSICS
+# define C __exp2f_data.poly_scaled
+  /* N*x = k + r with r in [-1/2, 1/2] */
+  kd = roundtoint (xd); /* k */
+  ki = converttoint (xd);
+#else
+# define C __exp2f_data.poly
+# define SHIFT __exp2f_data.shift_scaled
+  /* x = k/N + r with r in [-1/(2N), 1/(2N)] */
+  kd = (double) (xd + SHIFT); /* Rounding to double precision is required.  */
+  ki = asuint64 (kd);
+  kd -= SHIFT; /* k/N */
+#endif
+  r = xd - kd;
+
+  /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+  t = T[ki % N];
+  ski = ki + sign_bias;
+  t += ski << (52 - EXP2F_TABLE_BITS);
+  s = asdouble (t);
+  z = C[0] * r + C[1];
+  r2 = r * r;
+  y = C[2] * r + 1;
+  y = z * r2 + y;
+  y = y * s;
+  return y;
+}
+
+/* Returns 0 if not int, 1 if odd int, 2 if even int.  */
+static inline int
+checkint (uint32_t iy)
+{
+  int e = iy >> 23 & 0xff;
+  if (e < 0x7f)
+    return 0;
+  if (e > 0x7f + 23)
+    return 2;
+  if (iy & ((1 << (0x7f + 23 - e)) - 1))
+    return 0;
+  if (iy & (1 << (0x7f + 23 - e)))
+    return 1;
+  return 2;
+}
+
+static inline int
+zeroinfnan (uint32_t ix)
+{
+  return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
+}
+
+float
+powf (float x, float y)
+{
+  unsigned long sign_bias = 0;
+  uint32_t ix, iy;
+
+  ix = asuint (x);
+  iy = asuint (y);
+  if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000
+			  || zeroinfnan (iy),
+			0))
+    {
+      /* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan).  */
+      if (__builtin_expect (zeroinfnan (iy), 0))
+	{
+	  if (2 * iy == 0)
+	    return ieee_2008_issignaling (x) ? x + y : 1.0f;
+	  if (ix == 0x3f800000)
+	    return ieee_2008_issignaling (y) ? x + y : 1.0f;
+	  if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000)
+	    return x + y;
+	  if (2 * ix == 2 * 0x3f800000)
+	    return 1.0f;
+	  if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
+	    return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf.  */
+	  return y * y;
+	}
+      if (__builtin_expect (zeroinfnan (ix), 0))
+	{
+	  float_t x2 = x * x;
+	  if (ix & 0x80000000 && checkint (iy) == 1)
+	    {
+	      x2 = -x2;
+	      sign_bias = 1;
+	    }
+#if WANT_ERRNO
+	  if (2 * ix == 0 && iy & 0x80000000)
+	    return __math_divzerof (sign_bias);
+#endif
+	  return iy & 0x80000000 ? 1 / x2 : x2;
+	}
+      /* x and y are non-zero finite.  */
+      if (ix & 0x80000000)
+	{
+	  /* Finite x < 0.  */
+	  int yint = checkint (iy);
+	  if (yint == 0)
+	    return __math_invalidf (x);
+	  if (yint == 1)
+	    sign_bias = SIGN_BIAS;
+	  ix &= 0x7fffffff;
+	}
+      if (ix < 0x00800000)
+	{
+	  /* Normalize subnormal x so exponent becomes negative.  */
+	  ix = asuint (x * 0x1p23f);
+	  ix &= 0x7fffffff;
+	  ix -= 23 << 23;
+	}
+    }
+  double_t logx = log2_inline (ix);
+  double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec.  */
+  if (__builtin_expect ((asuint64 (ylogx) >> 47 & 0xffff)
+			  >= asuint64 (126.0 * POWF_SCALE) >> 47,
+			0))
+    {
+      /* |y*log(x)| >= 126.  */
+      if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
+	return __math_oflowf (sign_bias);
+      if (ylogx <= -150.0 * POWF_SCALE)
+	return __math_uflowf (sign_bias);
+#if WANT_ERRNO_UFLOW
+      if (ylogx < -149.0 * POWF_SCALE)
+	return __math_may_uflowf (sign_bias);
+#endif
+    }
+  return (float) exp2_inline (ylogx, sign_bias);
+}
+#endif
diff --git a/newlib/libm/common/sf_pow_log2_data.c b/newlib/libm/common/sf_pow_log2_data.c
new file mode 100644
index 000000000..6467976e0
--- /dev/null
+++ b/newlib/libm/common/sf_pow_log2_data.c
@@ -0,0 +1,57 @@
+/* Data definition for powf.
+   Copyright (c) 2017 ARM Ltd.  All rights reserved.
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#ifndef OBSOLETE_MATH
+
+#include "math_config.h"
+
+const struct powf_log2_data __powf_log2_data = {
+  .tab = {
+  { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE },
+  { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE },
+  { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE },
+  { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE },
+  { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE },
+  { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE },
+  { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE },
+  { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE },
+  { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE },
+  { 0x1p+0, 0x0p+0 * POWF_SCALE },
+  { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE },
+  { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE },
+  { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE },
+  { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE },
+  { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE },
+  { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE },
+  },
+  .poly = {
+  0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE,
+  0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE,
+  0x1.71547652ab82bp0 * POWF_SCALE,
+  }
+};
+#endif
diff --git a/newlib/libm/math/Makefile.am b/newlib/libm/math/Makefile.am
index 9e8e92840..e745159ae 100644
--- a/newlib/libm/math/Makefile.am
+++ b/newlib/libm/math/Makefile.am
@@ -48,7 +48,8 @@ fsrc =	kf_rem_pio2.c \
 	sf_frexp.c sf_ldexp.c \
 	sf_signif.c sf_sin.c \
 	sf_tan.c sf_tanh.c \
-	wf_exp2.c wf_tgamma.c
+	wf_exp2.c wf_tgamma.c \
+	wf_log2.c
 
 lsrc = el_hypot.c
 
diff --git a/newlib/libm/math/Makefile.in b/newlib/libm/math/Makefile.in
index 8f76aad4e..1f5a69406 100644
--- a/newlib/libm/math/Makefile.in
+++ b/newlib/libm/math/Makefile.in
@@ -137,7 +137,8 @@ am__objects_2 = lib_a-kf_rem_pio2.$(OBJEXT) lib_a-kf_cos.$(OBJEXT) \
 	lib_a-sf_frexp.$(OBJEXT) lib_a-sf_ldexp.$(OBJEXT) \
 	lib_a-sf_signif.$(OBJEXT) lib_a-sf_sin.$(OBJEXT) \
 	lib_a-sf_tan.$(OBJEXT) lib_a-sf_tanh.$(OBJEXT) \
-	lib_a-wf_exp2.$(OBJEXT) lib_a-wf_tgamma.$(OBJEXT)
+	lib_a-wf_exp2.$(OBJEXT) lib_a-wf_tgamma.$(OBJEXT) \
+	lib_a-wf_log2.$(OBJEXT)
 am__objects_3 = lib_a-el_hypot.$(OBJEXT)
 @USE_LIBTOOL_FALSE@am_lib_a_OBJECTS = $(am__objects_1) \
 @USE_LIBTOOL_FALSE@	$(am__objects_2) $(am__objects_3)
@@ -169,7 +170,7 @@ am__objects_5 = kf_rem_pio2.lo kf_cos.lo kf_sin.lo kf_tan.lo \
 	wf_sincos.lo wf_drem.lo sf_asinh.lo sf_atan.lo sf_ceil.lo \
 	sf_cos.lo sf_erf.lo sf_fabs.lo sf_floor.lo sf_frexp.lo \
 	sf_ldexp.lo sf_signif.lo sf_sin.lo sf_tan.lo sf_tanh.lo \
-	wf_exp2.lo wf_tgamma.lo
+	wf_exp2.lo wf_tgamma.lo wf_log2.lo
 am__objects_6 = el_hypot.lo
 @USE_LIBTOOL_TRUE@am_libmath_la_OBJECTS = $(am__objects_4) \
 @USE_LIBTOOL_TRUE@	$(am__objects_5) $(am__objects_6)
@@ -372,7 +373,8 @@ fsrc = kf_rem_pio2.c \
 	sf_frexp.c sf_ldexp.c \
 	sf_signif.c sf_sin.c \
 	sf_tan.c sf_tanh.c \
-	wf_exp2.c wf_tgamma.c
+	wf_exp2.c wf_tgamma.c \
+	wf_log2.c
 
 lsrc = el_hypot.c
 libmath_la_LDFLAGS = -Xcompiler -nostdlib
@@ -1270,6 +1272,12 @@ lib_a-wf_tgamma.o: wf_tgamma.c
 lib_a-wf_tgamma.obj: wf_tgamma.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-wf_tgamma.obj `if test -f 'wf_tgamma.c'; then $(CYGPATH_W) 'wf_tgamma.c'; else $(CYGPATH_W) '$(srcdir)/wf_tgamma.c'; fi`
 
+lib_a-wf_log2.o: wf_log2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-wf_log2.o `test -f 'wf_log2.c' || echo '$(srcdir)/'`wf_log2.c
+
+lib_a-wf_log2.obj: wf_log2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-wf_log2.obj `if test -f 'wf_log2.c'; then $(CYGPATH_W) 'wf_log2.c'; else $(CYGPATH_W) '$(srcdir)/wf_log2.c'; fi`
+
 lib_a-el_hypot.o: el_hypot.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-el_hypot.o `test -f 'el_hypot.c' || echo '$(srcdir)/'`el_hypot.c
 
diff --git a/newlib/libm/math/ef_exp.c b/newlib/libm/math/ef_exp.c
index 6824f991a..4f8585145 100644
--- a/newlib/libm/math/ef_exp.c
+++ b/newlib/libm/math/ef_exp.c
@@ -15,6 +15,7 @@
 
 #include "fdlibm.h"
 
+#ifdef OBSOLETE_MATH
 #ifdef __v810__
 #define const
 #endif
@@ -97,3 +98,4 @@ P5   =  4.1381369442e-08; /* 0x3331bb4c */
 	    return y*twom100;
 	}
 }
+#endif
diff --git a/newlib/libm/math/ef_log.c b/newlib/libm/math/ef_log.c
index 619fe9090..c86e63529 100644
--- a/newlib/libm/math/ef_log.c
+++ b/newlib/libm/math/ef_log.c
@@ -15,6 +15,7 @@
 
 #include "fdlibm.h"
 
+#ifdef OBSOLETE_MATH
 #ifdef __STDC__
 static const float
 #else
@@ -90,3 +91,4 @@ static float zero   =  0.0;
 		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
 	}
 }
+#endif
diff --git a/newlib/libm/math/ef_pow.c b/newlib/libm/math/ef_pow.c
index b3041dbdc..ae84d7616 100644
--- a/newlib/libm/math/ef_pow.c
+++ b/newlib/libm/math/ef_pow.c
@@ -15,6 +15,7 @@
 
 #include "fdlibm.h"
 
+#ifdef OBSOLETE_MATH
 #ifdef __v810__
 #define const 
 #endif
@@ -253,3 +254,4 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 	else SET_FLOAT_WORD(z,j);
 	return s*z;
 }
+#endif
diff --git a/newlib/libm/math/wf_exp.c b/newlib/libm/math/wf_exp.c
index 70f4459b4..7d41f721a 100644
--- a/newlib/libm/math/wf_exp.c
+++ b/newlib/libm/math/wf_exp.c
@@ -18,6 +18,7 @@
  */
 
 #include "fdlibm.h"
+#ifdef OBSOLETE_MATH
 #include <errno.h>
 
 #ifdef __STDC__
@@ -101,3 +102,4 @@ u_threshold= -1.0397208405e+02;  /* 0xc2cff1b5 */
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif
diff --git a/newlib/libm/math/wf_exp2.c b/newlib/libm/math/wf_exp2.c
index 944031405..f635cef0c 100644
--- a/newlib/libm/math/wf_exp2.c
+++ b/newlib/libm/math/wf_exp2.c
@@ -18,6 +18,7 @@
  */
 
 #include "fdlibm.h"
+#ifdef OBSOLETE_MATH
 #include <errno.h>
 #include <math.h>
 
@@ -44,3 +45,4 @@
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif
diff --git a/newlib/libm/math/wf_log.c b/newlib/libm/math/wf_log.c
index 4518b863b..2d6f6550d 100644
--- a/newlib/libm/math/wf_log.c
+++ b/newlib/libm/math/wf_log.c
@@ -18,6 +18,7 @@
  */
 
 #include "fdlibm.h"
+#ifdef OBSOLETE_MATH
 #include <errno.h>
 
 #ifdef __STDC__
@@ -84,3 +85,4 @@
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif
diff --git a/newlib/libm/math/wf_log2.c b/newlib/libm/math/wf_log2.c
new file mode 100644
index 000000000..1f8323ae4
--- /dev/null
+++ b/newlib/libm/math/wf_log2.c
@@ -0,0 +1,50 @@
+/* wf_log2.c -- float version of s_log2.c.
+ * Modification of sf_exp10.c by Yaakov Selkowitz 2009.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+/* 
+ * wrapper log2f(x)
+ */
+
+#include "fdlibm.h"
+#ifdef OBSOLETE_MATH
+#include <errno.h>
+#include <math.h>
+#undef log2
+#undef log2f
+
+#ifdef __STDC__
+	float log2f(float x)		/* wrapper log2f */
+#else
+	float log2f(x)			/* wrapper log2f */
+	float x;
+#endif
+{
+  return (logf(x) / (float_t) M_LN2);
+}
+
+#ifdef _DOUBLE_IS_32BITS
+
+#ifdef __STDC__
+	double log2(double x)
+#else
+	double log2(x)
+	double x;
+#endif
+{
+	return (double) log2f((float) x);
+}
+
+#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif
diff --git a/newlib/libm/math/wf_pow.c b/newlib/libm/math/wf_pow.c
index a30f8808e..dde074804 100644
--- a/newlib/libm/math/wf_pow.c
+++ b/newlib/libm/math/wf_pow.c
@@ -18,6 +18,7 @@
  */
 
 #include "fdlibm.h"
+#ifdef OBSOLETE_MATH
 #include <errno.h>
 
 #ifdef __STDC__
@@ -177,3 +178,4 @@
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif

Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Corinna Vinschen]

[-- Attachment #1: Type: text/plain, Size: 1771 bytes --]

Hi Szabolcs,

On Aug 30 15:18, Szabolcs Nagy wrote:
> Based on code from https://github.com/ARM-software/optimized-routines/
> 
> This patch adds a highly optimized generic implementation of expf,
> exp2f, logf, log2f and powf.  The new functions are not only
> significantly faster, but are also smaller, more accurate and fix
> several correctness issues.  In order to achieve this, the algorithm
> uses double precision arithmetic for accuracy, avoids divisions and
> uses small table lookups to minimize the polynomials.  Special cases
> are handled inline to avoid the unnecessary overhead of wrapper
> functions and set errno to POSIX requirements.
> 
> The new functions are added under newlib/libm/common and are
> currently enabled for AArch64 and AArch32 with VFP format.  The
> new functions are written in C99 and do not support non-IEEE
> representations, mixed endian doubles or non-standard errno setting.
> Targets can enable the new math code by undefining OBSOLETE_MATH.
> Targets with a single precision FPU may still prefer the old
> implementation. It was not clear what's the best way to add such
> alternative math implementations to newlib so this is an RFC
> patch and feedback is welcome.

I'm not confident enough with math stuff to review this, so I'd
rather like to defer to Jeff here.

However, two points:

- Please send the patch as generated by `git format-patch'.  Ideally
  as a patchset of smaller patches.

- Why the OBSOLETE_MATH stuff?  If these implementations are generic
  and sufficiently tested, wouldn't it make sense to enable them by
  default without forcing other targets to enable the OBSOLETE_MATH
  setting?


Thanks,
Corinna

-- 
Corinna Vinschen
Cygwin Maintainer
Red Hat

[-- Attachment #2: signature.asc --]
[-- Type: application/pgp-signature, Size: 819 bytes --]

Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Joel Sherrill]

On 8/30/2017 10:04 AM, Corinna Vinschen wrote:
> Hi Szabolcs,
> 
> On Aug 30 15:18, Szabolcs Nagy wrote:
>> Based on code from https://github.com/ARM-software/optimized-routines/
>>
>> This patch adds a highly optimized generic implementation of expf,
>> exp2f, logf, log2f and powf.  The new functions are not only
>> significantly faster, but are also smaller, more accurate and fix
>> several correctness issues.  In order to achieve this, the algorithm
>> uses double precision arithmetic for accuracy, avoids divisions and
>> uses small table lookups to minimize the polynomials.  Special cases
>> are handled inline to avoid the unnecessary overhead of wrapper
>> functions and set errno to POSIX requirements.
>>
>> The new functions are added under newlib/libm/common and are
>> currently enabled for AArch64 and AArch32 with VFP format.  The
>> new functions are written in C99 and do not support non-IEEE
>> representations, mixed endian doubles or non-standard errno setting.
>> Targets can enable the new math code by undefining OBSOLETE_MATH.
>> Targets with a single precision FPU may still prefer the old
>> implementation. It was not clear what's the best way to add such
>> alternative math implementations to newlib so this is an RFC
>> patch and feedback is welcome.
> 
> I'm not confident enough with math stuff to review this, so I'd
> rather like to defer to Jeff here.
> 
> However, two points:
> 
> - Please send the patch as generated by `git format-patch'.  Ideally
>    as a patchset of smaller patches.
> 
> - Why the OBSOLETE_MATH stuff?  If these implementations are generic
>    and sufficiently tested, wouldn't it make sense to enable them by
>    default without forcing other targets to enable the OBSOLETE_MATH
>    setting?

Any comment on the difference in code and data size? Just curious
if we are considering it on all targets.

What capabilities does it require of the target architecture? You
mentioned VFP. Does it require vector operations. If something
is assumed, if the minimum capabilities are not met, how well
does this code perform?

> 
> 
> Thanks,
> Corinna
> 

--joel

Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Jeff Johnston]

On Wed, Aug 30, 2017 at 11:04 AM, Corinna Vinschen <vinschen@redhat.com> wrote:
> Hi Szabolcs,
>
> On Aug 30 15:18, Szabolcs Nagy wrote:
>> Based on code from https://github.com/ARM-software/optimized-routines/
>>
>> This patch adds a highly optimized generic implementation of expf,
>> exp2f, logf, log2f and powf.  The new functions are not only
>> significantly faster, but are also smaller, more accurate and fix
>> several correctness issues.  In order to achieve this, the algorithm
>> uses double precision arithmetic for accuracy, avoids divisions and
>> uses small table lookups to minimize the polynomials.  Special cases
>> are handled inline to avoid the unnecessary overhead of wrapper
>> functions and set errno to POSIX requirements.
>>
>> The new functions are added under newlib/libm/common and are
>> currently enabled for AArch64 and AArch32 with VFP format.  The
>> new functions are written in C99 and do not support non-IEEE
>> representations, mixed endian doubles or non-standard errno setting.
>> Targets can enable the new math code by undefining OBSOLETE_MATH.
>> Targets with a single precision FPU may still prefer the old
>> implementation. It was not clear what's the best way to add such
>> alternative math implementations to newlib so this is an RFC
>> patch and feedback is welcome.
>
> I'm not confident enough with math stuff to review this, so I'd
> rather like to defer to Jeff here.
>

I noticed that the ARM routines these are based on have an Apache
license.  I also
noted that you were the one who wrote the patches to that code that
has become the newlib implementations.
When modifying old code, you must keep the old license unless all the
authors and license owner agree to
relicense it.  In this case, ARM is the owner of the initial license
and so you probably should stick with the same license or
bounce it off your employer to make sure it is ok.

Can you comment on the correctness issues above?  Are there blatant
errors in the current implementation that should be
looked at (as opposed to rounding and "level of C Standard supported" issues)?

IMO, opting-in is reasonable considering that some platforms will not
meet the criteria and will break unless someone does the
work to go through and configure them properly.  For example, do all
the embedded compilers support hex floating-point constants by
this point?

-- Jeff J.

> However, two points:
>
> - Please send the patch as generated by `git format-patch'.  Ideally
>   as a patchset of smaller patches.
>
> - Why the OBSOLETE_MATH stuff?  If these implementations are generic
>   and sufficiently tested, wouldn't it make sense to enable them by
>   default without forcing other targets to enable the OBSOLETE_MATH
>   setting?
>
>
> Thanks,
> Corinna
>
> --
> Corinna Vinschen
> Cygwin Maintainer
> Red Hat

Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Szabolcs Nagy]

On 30/08/17 19:12, Jeff Johnston wrote:
> I noticed that the ARM routines these are based on have an Apache
> license.  I also
> noted that you were the one who wrote the patches to that code that
> has become the newlib implementations.
> When modifying old code, you must keep the old license unless all the
> authors and license owner agree to
> relicense it.  In this case, ARM is the owner of the initial license
> and so you probably should stick with the same license or
> bounce it off your employer to make sure it is ok.
> 

arm is opensourcing this code under multiple licenses.

arm contribution policy to newlib used to use the 3 clause bsd license,
if you think this is a problem i can resend with apache license only.
or may be i should make multi-licensing clear in the upstream repo?

> Can you comment on the correctness issues above?  Are there blatant
> errors in the current implementation that should be
> looked at (as opposed to rounding and "level of C Standard supported" issues)?
> 

i thought the log2f and exp2f would have incorrect exception
behaviour, but on further investigation they look ok other
than incorrect exc.name setting for matherr.

powf is known to have some large ulp errors (>5 ulp), but i
haven't done extensive tests on newlib.

> IMO, opting-in is reasonable considering that some platforms will not
> meet the criteria and will break unless someone does the
> work to go through and configure them properly.  For example, do all
> the embedded compilers support hex floating-point constants by
> this point?
> 

yes i didn't want to enable it everywhere because there can
be lot of compatibility issues in embedded toolchains, but i
do want to enable it for aarch64 at least and on arm when the
new code is known to work.

Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Jeff Johnston]

On Fri, Sep 1, 2017 at 8:01 AM, Szabolcs Nagy <szabolcs.nagy@arm.com> wrote:
> On 30/08/17 19:12, Jeff Johnston wrote:
>> I noticed that the ARM routines these are based on have an Apache
>> license.  I also
>> noted that you were the one who wrote the patches to that code that
>> has become the newlib implementations.
>> When modifying old code, you must keep the old license unless all the
>> authors and license owner agree to
>> relicense it.  In this case, ARM is the owner of the initial license
>> and so you probably should stick with the same license or
>> bounce it off your employer to make sure it is ok.
>>
>
> arm is opensourcing this code under multiple licenses.
>
> arm contribution policy to newlib used to use the 3 clause bsd license,
> if you think this is a problem i can resend with apache license only.
> or may be i should make multi-licensing clear in the upstream repo?

I'm fine with the license as long as ARM is ok.  If you want to
clarify the multiple licenses somewhere
upstream, that might be helpful in the future.

>
>> Can you comment on the correctness issues above?  Are there blatant
>> errors in the current implementation that should be
>> looked at (as opposed to rounding and "level of C Standard supported" issues)?
>>
>
> i thought the log2f and exp2f would have incorrect exception
> behaviour, but on further investigation they look ok other
> than incorrect exc.name setting for matherr.
>
> powf is known to have some large ulp errors (>5 ulp), but i
> haven't done extensive tests on newlib.
>
>> IMO, opting-in is reasonable considering that some platforms will not
>> meet the criteria and will break unless someone does the
>> work to go through and configure them properly.  For example, do all
>> the embedded compilers support hex floating-point constants by
>> this point?
>>
>
> yes i didn't want to enable it everywhere because there can
> be lot of compatibility issues in embedded toolchains, but i
> do want to enable it for aarch64 at least and on arm when the
> new code is known to work.
>

I'm fine with the patch.  Corinna, do you still want the opt-in removed or can
it be checked in?

-- Jeff J.

Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Corinna Vinschen]

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On Sep  1 11:30, Jeff Johnston wrote:
> On Fri, Sep 1, 2017 at 8:01 AM, Szabolcs Nagy <szabolcs.nagy@arm.com> wrote:
> > On 30/08/17 19:12, Jeff Johnston wrote:
> >> I noticed that the ARM routines these are based on have an Apache
> >> license.  I also
> >> noted that you were the one who wrote the patches to that code that
> >> has become the newlib implementations.
> >> When modifying old code, you must keep the old license unless all the
> >> authors and license owner agree to
> >> relicense it.  In this case, ARM is the owner of the initial license
> >> and so you probably should stick with the same license or
> >> bounce it off your employer to make sure it is ok.
> >>
> >
> > arm is opensourcing this code under multiple licenses.
> >
> > arm contribution policy to newlib used to use the 3 clause bsd license,
> > if you think this is a problem i can resend with apache license only.
> > or may be i should make multi-licensing clear in the upstream repo?
> 
> I'm fine with the license as long as ARM is ok.  If you want to
> clarify the multiple licenses somewhere
> upstream, that might be helpful in the future.
> 
> >
> >> Can you comment on the correctness issues above?  Are there blatant
> >> errors in the current implementation that should be
> >> looked at (as opposed to rounding and "level of C Standard supported" issues)?
> >>
> >
> > i thought the log2f and exp2f would have incorrect exception
> > behaviour, but on further investigation they look ok other
> > than incorrect exc.name setting for matherr.
> >
> > powf is known to have some large ulp errors (>5 ulp), but i
> > haven't done extensive tests on newlib.
> >
> >> IMO, opting-in is reasonable considering that some platforms will not
> >> meet the criteria and will break unless someone does the
> >> work to go through and configure them properly.  For example, do all
> >> the embedded compilers support hex floating-point constants by
> >> this point?
> >>
> >
> > yes i didn't want to enable it everywhere because there can
> > be lot of compatibility issues in embedded toolchains, but i
> > do want to enable it for aarch64 at least and on arm when the
> > new code is known to work.
> >
> 
> I'm fine with the patch.  Corinna, do you still want the opt-in removed or can
> it be checked in?

It's a bit worrysome that we have a macro OBSOLETE_MATH hidden
in an easy forgettable header.  It's nice and all that we get
better math functions for arm, but given that the code is generic,
I think every effort should be made to make sure all targets
get the new code.

Also, it would be nice to discuss Joel's questions.


Corinna

-- 
Corinna Vinschen
Cygwin Maintainer
Red Hat

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Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Corinna Vinschen]

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On Sep  5 00:18, Wilco Dijkstra wrote:
> Hi,
> 
> > Any comment on the difference in code and data size? Just curious
> > if we are considering it on all targets.
> 
> When statically linking with GLIBC, I noticed text size of binaries using
> Szabolc's patch was around 1200 bytes smaller on AArch64 when using
> expf, logf and powf. Newlib uses an almost identical fdlibm version so the
> savings should be similar. Compile it on your favourite target, YMMV.
> 
> > What capabilities does it require of the target architecture? You
> > mentioned VFP. Does it require vector operations. If something
> > is assumed, if the minimum capabilities are not met, how well
> > does this code perform?
> 
> Very little, if double precision operations have similar performance as
> single precision, you will get a huge speedup. The source is standard C99
> so it doesn't require any vector extensions. What is required is decent
> support for uint64_t, so it works best on 32/64-bit ISAs.
> 
> For 8/16-bit ISAs or CPUs without hardware floating point you generally
> have to use integer arithmetic using a fast 32x32->64 bit multiplier, but
> that requires a different algorithm. If your CPU doesn't have a multiplier(!?!)
> then CORDIC is your only option. However newlib isn't optimizing for these
> targets today, so this patch isn't aiming to either.
> 
> Mixed-endian IEEE formats could be supported but the various asuint()
> functions would need porting (same for issignaling). Non-IEEE formats would
> be harder given the use of integer masking to manipulate floating point values.
> 
> Wilco

Ok, I retract my reservations against OBSOLETE_MATH as such.  However,
there are a few problems with the current patch:

- Rename to __OBSOLETE_MATH (two underscores) so as not to spoil the
  namespace.

- The current implementation disallows a developer to override the
  setting from, e. g., sys/config.h or the command line.  As a minimum,
  __OBSOLETE_MATH should only be set if it isn't already set, and the
  checks for __OBSOLETE_MATH should check for being != 0:

  - #define __TGT_OBSOLETE_MATH 1 in arm and aarch cases

  - At the end of the file

    #ifndef __OBSOLETE_MATH
    #define __OBSOLETE_MATH __TGT_OBSOLETE_MATH
    #endif
  
  - Further checks in the code:

    #if __OBSOLETE_MATH

    rather than

    #ifdef __OBSOLETE_MATH

- The header of ieeefp.h explains the options.  Add __TGT_OBSOLETE_MATH /
  __OBSOLETE_MATH and add an informative comment along the lines of the
  above text, so developers have enough info to decide if they want to
  enable this for their target.

Not sure if __TGT_OBSOLETE_MATH is a good name, though.  I'm open for
better suggestions.


Thanks,
Corinna

-- 
Corinna Vinschen
Cygwin Maintainer
Red Hat

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Re: [RFC][PATCH] New expf, exp2f, logf, log2f and powf implementations

[Wilco Dijkstra]

Hi,

> Any comment on the difference in code and data size? Just curious
> if we are considering it on all targets.

When statically linking with GLIBC, I noticed text size of binaries using
Szabolc's patch was around 1200 bytes smaller on AArch64 when using
expf, logf and powf. Newlib uses an almost identical fdlibm version so the
savings should be similar. Compile it on your favourite target, YMMV.

> What capabilities does it require of the target architecture? You
> mentioned VFP. Does it require vector operations. If something
> is assumed, if the minimum capabilities are not met, how well
> does this code perform?

Very little, if double precision operations have similar performance as
single precision, you will get a huge speedup. The source is standard C99
so it doesn't require any vector extensions. What is required is decent
support for uint64_t, so it works best on 32/64-bit ISAs.

For 8/16-bit ISAs or CPUs without hardware floating point you generally
have to use integer arithmetic using a fast 32x32->64 bit multiplier, but
that requires a different algorithm. If your CPU doesn't have a multiplier(!?!)
then CORDIC is your only option. However newlib isn't optimizing for these
targets today, so this patch isn't aiming to either.

Mixed-endian IEEE formats could be supported but the various asuint()
functions would need porting (same for issignaling). Non-IEEE formats would
be harder given the use of integer masking to manipulate floating point values.

Wilco